Question: Simplify the following expression: $\sqrt{13}+\sqrt{208}-\sqrt{52}$
Solution: First, try to factor any perfect squares out of the radicals. $= \sqrt{13}+\sqrt{208}-\sqrt{52}$ $= \sqrt{13}+\sqrt{16 \cdot 13}-\sqrt{4 \cdot 13}$ Separate the radicals and simplify. $= \sqrt{13}+\sqrt{16} \cdot \sqrt{13}-\sqrt{4} \cdot \sqrt{13}$ $= \sqrt{13}+4\sqrt{13}-2\sqrt{13}$ Finally, simplify by combining the terms. $= ( 1 + 4 - 2 )\sqrt{13} = 3\sqrt{13}$